Three-Axis Accelerometer

Implement three-axis accelerometer

Library

GNC/Navigation

Description

The Three-Axis Accelerometer block implements an accelerometer
on each of the three axes. The ideal measured accelerations (A¯imeas) include the acceleration in
body axes at the center of gravity (A¯b),
lever arm effects due to the accelerometer not being at the center
of gravity, and, optionally, gravity in body axes can be removed.

A¯imeas=A¯b+ω¯b×(ω¯b×d¯)+ω¯˙b×d¯−g¯

where ω¯b are body-fixed angular rates, ω¯˙b are body-fixed angular accelerations
and d¯ is the lever arm. The lever
arm (d¯) is defined as the distances
that the accelerometer group is forward, right and below the center
of gravity.

d¯=[dxdydz]=[−(xacc−xCG)yacc−yCG−(zacc−zCG)]

The orientation of the axes used to determine the location of
the accelerometer group (xacc, yacc, zacc)
and center of gravity (xCG, yCG, zCG)
is from the zero datum (typically the nose) to aft, to the right of
the vertical centerline and above the horizontal centerline. The x-axis
and z-axis of this measurement axes are opposite
the body-fixed axes producing the negative signs in the lever arms
for x-axis and z-axis.

Measured accelerations (A¯meas)
output by this block contain error sources and are defined as

A¯meas=A¯imeas×A¯SFCC+A¯bias+noise

where A¯SFCC is a 3-by-3 matrix of scaling
factors on the diagonal and misalignment terms in the nondiagonal,
and A¯biasare the biases.

Optionally discretizations can be applied to the block inputs
and dynamics along with nonlinearizations of the measured accelerations
via a Saturation block.

Parameters

Units

Specifies the input and output units:

Units

Acceleration

Length

Metric (MKS)

Meters per second squared

Meters

English

Feet per second squared

Feet

Accelerometer location

The location of the accelerometer group is measured from the
zero datum (typically the nose) to aft, to the right of the vertical
centerline and above the horizontal centerline. This measurement reference
is the same for the center of gravity input. The units are in selected
length units.

Subtract
gravity

Select to subtract gravity from acceleration readings.

Second order dynamics

Select to apply second-order dynamics to acceleration readings.

Natural frequency (rad/sec)

The natural frequency of the accelerometer. The units of natural
frequency are radians per second.

Damping
ratio

The damping ratio of the accelerometer. A dimensionless parameter.

Scale factors and
cross-coupling

The 3-by-3 matrix used to skew the accelerometer from body axes
and to scale accelerations along body axes.

Measurement
bias

The three-element vector containing long-term biases along the
accelerometer axes. The units are in selected acceleration units.

Update
rate (sec)

Specify the update rate of the accelerometer. An update rate
of 0 will create a continuous accelerometer. If noise is selected
and the update rate is 0, then the noise will be updated at the rate
of 0.1. The units of update rate are seconds.

If you:

Update this parameter value to 0 (continuous)

Configure a fixed-step solver for the model

Do not have a Control System Toolbox™ license

you must also select the Automatically handle rate
transition for data transfer check box in the Solver pane.
This check box enables the software to handle rate transitions correctly.

Noise
on

Select to apply white noise to acceleration readings.

Noise
seeds

The scalar seeds for the Gaussian noise generator for each axis
of the accelerometer.

Noise
power

The height of the PSD of the white noise for each axis of the
accelerometer. The units are:

(m/s2)/Hz for Metric
(MKS)

(ft/s2)/Hz for English

Lower and upper output
limits

The six-element vector containing three minimum values and three
maximum values of acceleration in each of the accelerometer axes.
The units are in selected acceleration units.

Inputs and Outputs

Input

Dimension
Type

Description

First

Three-element vector

Contains the actual accelerations in body-fixed axes, in selected
units.

Second

Three-element vector

Contains the angular rates in body-fixed axes, in radians per
second.

Third

Three-element vector

Contains the angular accelerations in body-fixed axes, in radians
per second squared.

Fourth

Three-element vector

Contains the location of the center of gravity, in selected
units.

Fifth (Optional)

Three-element vector

Contains the gravity in body axis, in selected units.

Output

Dimension
Type

Description

First

Three-element vector

Contains the measured accelerations from the accelerometer,
in selected units.

Assumptions and Limitations

Vibropendulous error and hysteresis effects are not accounted
for in this block. Additionally, this block is not intended to model
the internal dynamics of different forms of the instrument.

Note:
This block requires the Control System Toolbox product for
discrete operation (nonzero sample time).